According to the aid agency's estimates, 340,000 people - approximately a third of Mogadishu's inhabitants - have fled their homes while those who remain face rapidly deteriorating conditions.
The Supreme Council of Islamic Courts - which controlled much of the country for six months last year - and government troops reinforced by neighbouring Ethiopia have been involved in escalating clashes since the start of the year.
"We deplore the indiscriminate shelling of a medical facility," said Christian Balslev-Olesen, UNICEF's Representative in Somalia.
"It is an action that is totally unacceptable and one for which no justification can be given."
With supplies impossible to distribute effectively in such a situation, UNICEF claims that disease is beginning to rival violence as a cause of death in the country.
There have been almost 17,000 case of acute diarrhoea in the central and southern regions of the country with 593 deaths and nearly 40 confirmed cases of cholera.
An appeal to raise $11.5 million to help meet the nutrition, health, education and protection needs of children affected by the conflict has just been launched.
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